Zero G without a spacecraft
Published on Jan 7, 2009 at 9:46 pm.
6 Comments.
Filed under NASA, aeronautics, microgravity flight, physics.
Everyone is familiar with images sent back to Earth of astronauts frolicking in the weightless environment of a spacecraft. When John Glenn was in orbit around Earth, he radioed back to mission controllers on the ground that he was experiencing “Zero G and I feel fine.” But, do you really have to go into space in order to experience zero G? The answer, it turns out, is no.
To explain this, we need to first understand how we experience the effect of gravity. So, bear with me as I explain a few things that I talk about in my first semester physics class. The gravitational force acts between any two bodies that have mass. For the purposes of this posting, I will concentrate on just the neighborhood of Earth (that being anywhere within a few thousand miles of the surface of the Earth). In this neighborhood, the Earth itself is the biggest thing around, by far, and, of course, has the most mass. So, most of the gravity that we experience is the effect of the gravitational force between Earth and an object. Now, the Sun is pretty big, too, and despite being so far away, it also has an effect, as does the Moon. The gravitational effect of the Moon, of course, is why we have tides. The Sun’s gravity also creates tides, though they are smaller than those created by the Moon. The strength of the gravitational force between two bodies is given by Newton’s Universal Law of gravitation, seen here.
In this equation, G is the universal gravitational constant, the m’s are the two masses, and r is the distance between the two bodies.
This is the force between two bodies. Now, the effect of an isolated or unbalanced force on a body is given by Newton’s Second Law, seen here. 
The effect is to yield an acceleration. If we solve Newton’s second law for the acceleration, we find that it is given by dividing the magnitude of the force by the mass. But the force is given by the Universal Law of Gravitation, above. Let the mass, m1, be the mass of the object and the mass, m2, be the mass of the Earth. Plug the Universal Law of gravitation into the equation a = F/m and let the m be m1, the mass of the object. You can see that the mass of the object is in both the numerator and the denominator, so it cancels. 
What is left is the universal gravitational constant, the mass of the Earth, and the distance between the center of the Earth and the object (which is basically the radius of the Earth). Plugging in numbers, you get a value for the acceleration due to gravity of 9.8 m/s2. As long as you don’t go many decimal places, this is pretty constant across the surface of the Earth and anywhere within a few kilometers of the surface of the Earth. Since it always 
gives the same value, we call this acceleration “g”. If you drop something, then this gives the acceleration of the object towards the ground. But, that means that gravity is pulling on it, of course. If you go back to Newton’s Second Law and plug g in for the acceleration, you see that the force due to gravity on an object is given by F = mg. This force due to gravity is called the weight of an object.
Now, this is all fine. But, on the surface of the Earth, the force due to gravity is seldom unbalanced. When something is sitting on a table, the floor, or whatever, gravity tries to pull the object downward, but there is something in the way of it moving. The electrons of the surface repel the electrons of the object, and when the forces balance out, the object just sits there. This is called the Normal force (normal means “perpendicular” in mathematics, and the force acts perpendicular to the surface). 
So, if you are standing on the ground, then the ground pushes up on you with a force equal to your weight. That is your experience of weight: the ground pushing back upward on you. If you are sitting in a seat that suddenly accelerates forward at 19.6 m/s2 (twice the acceleration due to gravity), then you would feel the seat pushing forward on you with a force double what it would feel like if you were laying on your back in the seat. We would say that the seat is pushing on you with a force of two G’s. If you are in an elevator that is accelerating upward, then the floor of the elevator has to push upward with a force equal to your own weight plus a little more in order for you to accelerate upward with the elevator. It would feel to you as if you weighed a bit more (and that is exactly what it would seem to be the case if you were standing on a scale), or alternately, it would feel as if gravity were suddenly a little stronger. Conversely, if the elevator were accelerating downward, then the floor of the elevator would push a little less strongly on you, and you would feel lighter or as if gravity had suddenly become weaker.
In fact, this gets to a very interesting point that Albert Einstein realized. You really cannot tell the difference between acceleration and gravity. When the elevator goes up, you feel heavier, and unless you knew that you were in an elevator going upward and that the gravitation force of the Earth were not likely to suddenly increase, then there would be no way to tell the difference. This gives rise to all sorts of interesting phenomena that exist in a gravitational field, such as time dilation, the bending of light by gravity, and all sorts of other interesting effects. This is the field of general relativity, and it is well beyond what I want to talk about in this blog posting.
But, consider an astronaut aboard an orbiting spacecraft. As the spacecraft is moving along, gravity still pulls on it. The Earth’s gravity doesn’t just suddenly end at the edge of the atmosphere. For one thing, the atmosphere doesn’t actually have an edge. It is a gas (or actually, a collection of gases). So, it just gets thinner and thinner, until it is eventually so thin that pretty much everyone agrees that it is too thin to think of it in the same manner that we do here on the ground. At the altitude that the International Space Station or the Space Shuttle orbits the air is so thin that we think of that altitude as being “above the atmosphere.” So, there is still gravity at that altitude. Thus, as the ISS or the Space Shuttle is moving along, Earth’s gravity acts on it (and the astronauts aboard). That force causes the spacecraft to fall towards the Earth. That causes the path to be curved. But, the spacecraft is moving so quickly that the surface of the Earth curves away under it. And, the force of gravity continues to act towards the center of the Earth. 
If the spacecraft is moving along quickly enough, the path forms a circle, with Earth at the center and gravity always pulling towards the center of the circle. The spacecraft is falling towards Earth, but it is moving to the side so fast that it keeps missing. (In fact, in order to reenter the atmosphere, the Space Shuttle slows down so that it quits missing the Earth.) Since the spacecraft, the astronauts, and all the contents aboard the spacecraft are all moving together, and there is no force on anything to keep them from accelerating towards Earth at the acceleration due to gravity, then nobody and nothing aboard feels a force against gravity. Thus, nobody and nothing feels a force that counters gravity, so they don’t feel the force that we all experience here on the surface of the Earth that makes us experience weight. It would be like an elevator in free fall. There would be no force acting from the floor on the person in the elevator, and so they would feel no weight at all. It would feel to them as if the Earth’s gravity had turned off! Likewise aboard the spacecraft, the astronauts and contents would feel weightless. We often, like John Glenn, say that the astronauts are experiencing Zero G.
Actually, all of this assumes a perfectly circular orbit, and it neglects the much smaller effects of gravity from other bodies, such as the Sun, Moon, and even the other objects aboard the spacecraft. Since this ideal situation is never actually realized, NASA doesn’t really use the term “Zero G” to refer to this apparent weightlessness. Rather, they use the term microgravity to refer to the experience of near zero G conditions.
Now, suppose that you had an aircraft that was flying along in level flight. If you were on board the aircraft, then the deck of the aircraft would be pushing up on you to compensate for the effect of the gravitational force (so that you fly straight and level with the aircraft). But, what if the aircraft is accelerating upward? Then, the deck of the aircraft would have to push upward on you more than gravity is pulling downward, and you’d feel heavier (like in the elevator accelerating upward). And, if the aircraft were accelerating downward, then you’d feel lighter just as you would in the elevator accelerating downward. Note that the key term here is accelerating. It is not enough that the aircraft (or elevator) be moving upward or downward. It has to be be accelerating, or changing the speed at which it is moving upward or downward. So, an aircraft can be moving upward, but still accelerating downward (slowing the upward motion) or moving downward and speedup up its downward motion. Both kinds of motion involve downward acceleration, and it would feel exactly the same in the aircraft. 
For an aircraft moving to the side at a near constant speed, the changing upward or downward speed makes the path of the aircraft appear as a parabola when viewed from the side.
Now, what would happen if an aircraft were to be in a parabola as shown here in which the aircraft were accelerating downward at a constant rate equal to g, the acceleration due to gravity? The result would be that inside the aircraft, it would feel exactly as weightless as it would inside a spacecraft in orbit around the Earth. The occupants and everything aboard would experience zero G. Now, an aircraft can’t keep this up for long, though. Eventually, the parabola would arch over and intersect the ground. If the aircraft were still flying the parabola, that would be bad. But, for a minute or two, the aircraft would be experiencing zero G. In practice, though, for safety’s sake, you’d want to keep the time of zero G to under a minute so that you have time to pull out of the parabola.
Now, you can imagine that if astronauts and equipment is going to be flying in space under weightless conditions, then you’d want to test the equipment and train the astronauts as best you could under actual weightless conditions, if possible. Since an aircraft can experience such weightless conditions for a short time, that would make such a flight pretty useful for training and testing purposes, right? Well, NASA had that very idea. So, early in the history of the space program, NASA began to fly such flights aboard specially modified aircraft.
Over the years, there have been several such aircraft. Currently, NASA is using a C-9B aircraft based at Ellington Field, adjacent to the Johnson Space Center to conduct such flights (seen in the above photo). The aircraft is used for more than just flying astronauts around, though. It can be used by other researchers who have need of only about 30 seconds of weightlessness for an experiment. As it turns out, I happen to be one of those. As I write this posting, I am sitting in a hotel room near the space center. Next week, if all goes well, I will be flying an experiment aboard NASA’s C-9B aircraft. I plan on blogging about the training that will go into this and the things that we will be going through.
-Astroprof
Aircraft image courtesy NASA
CameronP on January 8, 2009 at 11:42 am: 1
That’s amazing! Good luck!
Sili on January 8, 2009 at 3:56 pm: 2
Good luck!
Isn’t the atmosphere still dense enough to cause drag on the ISS? I thought that was why it needed occasional reboosting.
Astroprof on January 8, 2009 at 5:37 pm: 3
Sili,
You are exactly right. That thin atmosphere is also why we need to boost the Hubble telescope to a higher orbit, too, or else it will come down on its own. Still, we often think about those altitudes as “being in space.”
Astroprof’s Page » Zero G and feeling fine on January 14, 2009 at 5:02 pm: 4
[…] on time, and flew out over the Gulf of Mexico. There the aircraft performed the maneuvers that I wrote about a few days ago. We got a few minutes after takeoff until the parabolas started to get things out […]
Mary Fairley on June 7, 2009 at 1:03 pm: 5
I am wondering if you can shed some light on something I experienced as a child. My mother had taken my brothers and I to the doctor in Marked Tree, Arkansas which is smack on top of the New Madrid earthquake fault. While sitting in the waiting room, there was a sudden, 15 second or so downward pull that was felt by everyone in the clinic. No earth shaking as usually and frequently felt during a tremor. Just a strong sensation of downward pull. I have tried to google this and your article is as close to an explanation as I could find. Any thoughts? I appreciate a reply.
Astroprof on June 7, 2009 at 1:07 pm: 6
Sorry, Mary. I can’t really say what you felt. I could maybe guess that there was a slight up and down movement from a small tembler and people felt more of the up than the down, but that is just a guess.